P E R S P E C T I V E S
PHOENIX CENTER FOR ADVANCED LEGAL & ECONOMIC PUBLIC POLICY STUDIES
Piracy and Movie Revenues:
A Critical Review of A Tale of the Long Tail
George S. Ford, PhD
September 16, 2013
Introduction
Theft isn’t good for the victim. Yet, a recent
study on piracy entitled Piracy and Movie
Revenues: Evidence from Megaupload: A Tale of the
Long Tail? (hereinafter “Tale of the Long Tail”)
conducted by researchers at the University of
Munich and the Copenhagen Business School
serves up the counter-intuitive claim that piracy
may increase box office sales for some films.1 To
reach this conclusion, Tale of the Long Tail uses as
an experiment the January 2012 shutdown of
what was likely the single largest online
distributor of pirated content—the file sharing
website Megaupload.com.2
Using data on
weekend box office revenues for thousands of
films shown in about fifty countries, the authors
split this data into pre- and post-shutdown
periods, and then apply econometric methods to
test for a difference between the two samples,
attributed any observed change to the
shutdown.3
Naturally, as other studies have shown, the
expectation is that piracy, if anything, reduces
box office revenues, but the authors of the study
offer a surprising, counter-intuitive conclusion.4
Specifically, while the revenues of “small” and
“blockbuster” movies (defined in reference to
the number of theaters in which the film opened
using a country-specific penetration rate) were
mostly unaffected by the Megaupload
shutdown, Tale of the Long Tail claims that the
shutdown of the pirate site actually reduced box
office revenues for “mid-size” films.
The
PHOENIX CENTER PERSPECTIVES 13-05
authors contend that this result suggests that
pirated copies are a form of advertising (thus
increasing sales), but the promotional effect
applies only to films released in a middling
number of theaters.
Upon close inspection of Tale of the
Long Tail, … the “piracy helps box
office sales” result is revealed to be
an artifact of a poorly-designed
statistical model….
While the unexpected conclusion drew
significant media attention,5 the result is
sufficiently bizarre to make an audience of
professional economists suspicious. Indeed,
although theft may offer benefits to the thief,
economists generally do not normally view theft
as beneficial to the victim or to society as a
whole.6 Accordingly, a claim of such an effect
obviously faces a high evidentiary standard.
Upon close inspection of Tale of the Long Tail, it is
clear the authors have failed to meet this
burden. To the contrary, the “piracy helps box
office sales” result is an artifact of a poorlydesigned statistical model, which is, in part, a
consequence of the study’s authors ignoring the
basic economics of the box office. The defect in
the Tale of the Long Tail’s model is revealed in the
dubious implication of that model that a
P E R S P E C T I V E S
“blockbuster” movie (as the authors define it)
will earn no more revenue than a “small movie”
and far less revenue than a “mid size” movie. In
fact, according to the analysis in Tale of the Long
Tail, what the authors define to be a
“blockbuster” movie makes only one-fourth
(1/4) of the revenues of mid-sized movies.7 The
bizarre result about the benefits of piracy is
based upon this dubious implication of the
statistical model.
In this PERSPECTIVE, I detail this problem with
Tale of the Long Tail, and outline a few other
defects. There are far too many problems with
the study’s empirical approach to cover them all
in detail, including the fundamental question
regarding whether the general “before” and
“after” approach can identify the effect of piracy
generally, and whether the authors have
estimated a model capable of capturing the
effect.8 A thorough analysis of the study is
unnecessary since the study’s central (and most
controversial) finding is easily dismissed.
Box Office Economics
proportional to the revenues earned from ticket
sales (this is an unnecessary but simplifying
assumption). How should he allocate films
among venues?
In this case, the basic principle is obvious—the
exhibitor wishes to maximize the total of
revenues earned on the n screens. In the limit,
he will assign films to screens so that the
revenues earned per screen are similar: if one
screen showing film x earned far less than
another showing film y, then he should consider
replacing x with y when he is free to do so.
Although it is reasonable to assume that
showing the same film on many screens will
result in continually diluted demand, and a fall
in per screen revenues, the basic principle can be
simplified to read as follows: show each film
with sufficiently high demand (single screen
revenue) until, on the margin, each film being
exhibited has equal marginal revenue. This
problem is very familiar to economists, and
resembles the well-known problem of allocating
a total output among a group of factories with
varying cost structures.
To begin, let’s establish the basic principle of
profit maximization at the box office. Movie
distributors and exhibitors face the problem of
assigning available films to available screens, on
an ongoing basis. Although there are various
complications and constraints involved in these
processes, from the economic point-of-view this
problem has a very basic structure, and that
structure, in the limit, yields a very simple
characterization of profit-maximizing behavior.
This characterization, in turn, implies a series of
simple propositions about the relationships
between theater (or screen) exhibitions and film
revenues.9
It is precisely this economic
characterization which should be examined
statistically, and should form the basis of any
econometric analysis of this problem.
The defect in the Tale of the Long
Tail’s model is revealed in the
dubious implication of that model
that a “blockbuster” movie (as the
authors define it) will earn no more
revenue than a “small movie” and
far less revenue than a “mid size”
movie. In fact, according to the
analysis in Tale of the Long Tail,
what the authors define to be a
“blockbuster” movie makes only
one-fourth (1/4) of the revenues of
mid-sized movies.
For simplicity, suppose an exhibitor has k
potential films, which he may show on n > 1
potential screen venues. Further, suppose the
exhibition costs, royalties, and so on are
Although the actual problem of scheduling
movies and screens is more complex than this,
PHOENIX CENTER PERSPECTIVES 13-05
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the basic principle is a very powerful one. It can
also be tested, if only approximately. If this
conceptualization is correct, then one expects the
following to roughly hold true:
First, it should be possible to predict a film’s box
office revenues per weekend (or week) with
good accuracy using only the numbers of
screens on which the film is shown that week.
Although films “age” and become less popular
over time, rational exhibitors react to this
“aging” effect by reducing screens to keep the
income per screen roughly equal to that
available from other films.
Second, one should be able to explain a film’s
gross box office revenue fairly well using total
“screen weeks” the film is exhibited.
Third, deviations from a good fit for these
predictions should be related to, and explained
by, variables plausibly related to the other
constraints under which exhibitors and theaters
operate (producer contracts, holidays, cast
popularity, and so forth).
Figure 1. Revenues (R), Theaters (N)
lnR
20
15
10
5
0
0
1000
2000
3000
4000
5000
N
This process has a predictable effect on observed
revenues: we should expect that the number of
theaters in which a movie is displayed will be a
very good predictor of a movie’s (weekend) box
PHOENIX CENTER PERSPECTIVES 13-05
office revenue. In Figure 1, I show this to be
true. In the figure, the (natural log of) weekend
gross revenues (lnR) for a sample of 634 films
shown in the U.S. in the year 2010 are plotted
against the number of theaters (N) in which the
film appeared each weekend.10 Clearly, theater
count is a potent determinant of weekend
revenues.
To illustrate the point, let’s do some tests of the
observations listed above regarding the
expectations of the economics of the box office
by using some simple regression analysis. First,
using data for U.S. films over the 2003-2013 time
period, theater counts alone explain 87% of the
variability in weekend revenues.11 Second, the
total number of theater weeks (computed as
theaters multiplied by weeks played) explains
80% of gross box office revenue for the same set
of films. Thus, predications of the theory are
supported—box office revenues are determined,
in large part, by the number of theaters in which
a film is shown. This is the “first-order”
prediction of economic theory: when exhibitors
behave optimally, they strive to assign films to
screens so that the marginal profitability of each
exhibited film is equal.
Given the economics of the box
office …, it would seem a natural
starting point for a model
explaining box office revenues to
start with theater counts. Theater
counts explain almost all the
variation in weekend revenues (87%
in the simplest of models). Yet, this
is not what Tale of the Long Tail
does.
Implausible Implications
Given the economics of the box office just
described, and the relationship shown so clearly
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by Figure 1, it would seem a natural starting
point for a model explaining box office revenues
to start with theater counts. Theater counts
explain almost all the variation in weekend
revenues (87% in the simplest of models). Yet,
this is not what Tale of the Long Tail does.
Instead, the study replaces theater counts with a
variable measuring the number of theaters in
which a film is shown in its opening weekend.
The authors then divide this first-week theater
count by the largest first-week theater count in
the sample (for each country individually) so
that the variable is expressed in terms a countryspecific penetration rate.12
Tale of the Long Tail’s statistical
model implies that the revenue of a
“blockbuster” will be equal, and in
some cases below, the revenues of a
“small” film. *** This result is
obviously senseless.
This penetration variable plays a key role in the
study; it is used to assign “sizes” to the movies.
Size is important, since the controversial result
from Tale of the Long Tail regards the differential
impacts of piracy across the “size” of movies
(that is, mid-size movies are alleged to actually
benefit at the box office from piracy). If a movie
appears in most theaters (a penetration closer to
1.0), then it is labeled a “blockbuster”; whereas if
it appears in few theaters (a penetration rate
closer to 0.0), then it is labeled “small.”13 A midsize movie, then, lies in the middle between 0.0
and 1.0. Thus, this measure of first-week
“penetration” is the study’s measure of “size,” a
variable labeled “S” in the study. In effect, the
authors intend the variable to be a measure of
the exhibitors’ estimates of the market potential
of the film, made prior to any actual box office
feedback.
PHOENIX CENTER PERSPECTIVES 13-05
Tale of the Long Tail’s statistical model attempts
to explain weekend box office revenues using
this size variable (and a few other factors not
material to the counter-intuitive result, so I
ignore them). Recall that the sample is divided
into pre- and post-shutdown groups, and the
revenue-to-size relationship is estimated for
each group.
In Figure 2, I illustrate the
estimated relationship for the pre-shutdown
period (labeled “Pre”). The natural log of
revenue is on the vertical axis, and the size
variable S is on the horizontal.
Figure 2. Revenues and Movie Size
(Munich Study)
ln(R)
a = 0.57

Pre
r’
0
S
0.15
0.50
1.0
Your alarm bells might be ringing. The “Pre”
curve in Figure 2 is concave (a hump), and this
hump reaches its maximum for films opening in
57% of theaters.14 Let’s consider the implications
of this result. Tale of the Long Tail’s statistical
model implies that the revenue of a
“blockbuster” will be equal, and in some cases
below, the revenues of a “small” film.15 This can
be seen in the figure that shows equal revenues
(at r’) for a film shown in 15% of theaters or in
100% of theaters.16 This result is obviously
senseless. Blockbuster films appear in many
theaters and earn significantly higher revenues
than other films—that’s the definition of a
“blockbuster.” But in Tale of the Long Tail, the
authors claim that a movie which has limited
consumer interests (small size) potentially earns
just as much if not much more revenue as does a
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movie with great consumer interest appearing in
the vast majority of theaters.17
Furthermore, the study’s model implies that a
“mid size” film earns substantially greater
revenues than a “blockbuster” film (about fourtimes as much revenue). This result is simply
implausible. A statistical model which claims
that a “blockbuster” movie earns revenues
smaller than “mid-size” and many “small size”
movies point plainly to a bad statistical model
and the need to conduct diagnostics in an effort
to reformulate. The humped relationship in film
“size” is sufficient to dismiss the entire study.
I believe that one primary source of the dubious
result in the treatment of size in the model.
Even in the U.S., the study’s measure of size
isn’t measuring size at all. (The problems are
more profound in the international context.) A
few examples demonstrate the problem.
Consider the 2012 film Obama’s America. This
movie opened in only one theater, earning
$31,610. Since this was opening weekend, Tale of
the Long Tail would take this movie to be a
“small film,” holding its theater count to one
theater over the course of its run. However, in
the film’s eighth week, it grossed $7.5 million
from viewings in 2,017 theaters. It grossed $33
million over its box office run. This is no small
film. A similar case is the 2009 film The Princess
and the Frog, which opened in only two theaters
so again it would be considered a “small film”
by the study’s standard. Yet, the film went on to
gross $104 million and was shown in 3,475
theaters in a single weekend.
There are many other examples of this sort, like
the film Juno, which grossed $143 million but
opened in only seven theaters. On average,
about 70% of movies grossing over $100 million
will eventually appear in more theaters than
they open in. At the other end of the spectrum,
some movies earning less than $1 million
opened in thousands of theaters. While perhaps
these may be labeled exceptions, such
exceptions are caused by a poor modeling choice
PHOENIX CENTER PERSPECTIVES 13-05
and, thus, avoidable. Plainly, the S variable is a
poor measure of size, and a poor measure of
what actually determines weekend box office
revenues (mainly, theater or screen counts).
Box office data also belies the statistical model’s
results. In the U.S., the average film over the
2003-2013 period grossed $1.5 million if in about
700 theaters (S  0.15), $2.9 million if in about
2,500 theaters (S  0.57), and $24 million if in
almost every theater (> 4,250 theaters, S  1.0).18
There’s no hump in the relationship. Films
opening big do not earn one-quarter of the
revenues of films in 57% of theaters, or earn
revenues equal to films in 15% of theaters.
Something is obviously amuck in the study’s
model.19
…the study’s model implies that a
“mid size” film earns substantially
greater
revenues
than
a
“blockbuster” film (about fourtimes as much revenue). This result
is simply implausible. A statistical
model which claims that a
“blockbuster” movie earns revenues
smaller than “mid-size” and many
“small size” movies point plainly to
a bad statistical model and the need
to conduct diagnostics in an effort
to reformulate.
It is this mysterious result shown in Figure 2
that drives the counter-intuitive claim regarding
the benefits of piracy. In Figure 3, I add to
Figure 2 the “Post” revenue-to-size curve and
the difference between the “Pre” and “Post”
curves (the  curve, which is the marginal
effect). (See Figure 5 in Tale of the Long Tail for
comparison.) The Post curve exhibits the same
implausible property, with a maximum at 67%
of film “size.” As shown in the figure, the PostPAGE 5
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curve is flatter than the Pre curve, and its
maximum is shifted over.20
Figure 3 also illustrates the controversial effect
attributed by Tale of the Long Tail to the
Megaupload shutdown by the curve labeled ,
which is simply the subtraction of the Pre from
the Post curve. The U-shape of  implies that
the effect of the shutdown is positive for firms
with either a small S or a very large S, whereas
firms with a middling S see a revenue reduction
from the shutdown.
This is the study’s
proverbial “money shot.” (If fact, it is the only
shot, since the other results are quite weak.) As
stated in Tale of the Long Tail, “[t]he marginal
shutdown effect follows a u-shaped form in
movie size that is only significant for mediumsized movies.”21
Figure 3. Revenue, Size and the Marginal
Effect
ln(R)
a = 0.57


b = 0.67
Post
Pre

0
S
0.15
0.50
1.0
As made obvious by the figure, the counterintuitive U-shaped relationship is based
exclusively on the nonsensical hump-shaped
revenue-to-size
relationships.
As
a
consequence, the U-shape relationship is as
implausible as the humps—a statistical artifact
of a mis-specified model.
What I looked for and didn’t find in the Tale of
the Long Tail was some explanation as to what
effect piracy should have on the relationship
between penetration (or size) and weekend
PHOENIX CENTER PERSPECTIVES 13-05
revenues in the chosen model. Is piracy, or its
reduction, expected to have a particular
influence on the shape of the curve? On its
maximum? On small size film versus large
films?
No explanation or expectation is
provided, and this is problematic. (The authors
find something, and then make an attribution
unique to the result.) For example, given the
model’s specification (i.e., the quadratic
functional form), if the reduction in piracy has
the primary effect of increasing the revenues of
“blockbuster” films (films with a large S), but no
effect on small and mid-size films, then the
curve will shift in the same manner as shown in
the Figure 3 and the “mid-size” benefit
argument could appear.22 Yet, by definition,
there is no effect; the mid-size effect is purely a
statistical artifact of a mis-specified model. The
lack of a theoretical basis for this work prohibits
any meaningful interpretation of the results,
even if the statistical model wasn’t as defective
as it is.
It is difficult to accept that
exhibitors,
acting
in
an
economically
rational
manner,
would ever choose levels of
penetration that reduce film
revenues.
Results of this kind
should prompt a careful reexamination of the authors’ model.
The proper place to start is almost
always with the basic economic
principles involved.
The bizarre implications of the statistical model
regarding the revenue-to-size relationship
strongly suggest an underlying problem with
the specification. It is difficult to accept that
exhibitors, acting in an economically rational
manner, would ever choose levels of penetration
that reduce film revenues. Results of this kind
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P E R S P E C T I V E S
should prompt a careful re-examination of the
authors’ model. The proper place to start is
almost always with the basic economic
principles involved.
Empirics and Economics
As discussed above, under profit maximization,
the revenues of a movie will be related to the
number of theaters the movie plays in, not the
number of theaters it opens in. Theater count
alone explains 87% of the variation in weekend
revenues for a sample of movies appearing in
theaters over the period 2003-2013, and total
theater weeks over the box office live of a film
explain 80% of the variability in gross revenues.
Here, I compare the explanatory power of a
model explaining revenues in terms of theater
counts to the model used in the study. I limit
the sample to the U.S. films over the 2003-2011
period (to avoid the Megaupload shutdown).
…the benefit of the revenue-totheater/screen model is that it is
consistent with basic economic
theory; the Tale of the Long Tail’s
model is not. Revenues are not
determined by an opening week
penetration rate:
they are
determined by the number of
theaters (or screens) a movie is in.
From the discussion above we know that a
simple regression of log-revenues on log theater
counts explains 87% of the variation of the
dependent variable over this period, and the
model is plainly consistent with the pattern
shown in Figure 1.23 In contrast, the Tale of the
Long Tail’s model (including S, S2, and the
natural log of weeks in the theater) explains only
47% of the variability of log revenues of the U.S.
films over the 2003-2011 period. This evidence
strongly suggests that the study’s model could
PHOENIX CENTER PERSPECTIVES 13-05
be better specified and likely suffers from a
functional form mis-specification.24
More
importantly, the benefit of the revenue-totheater/screen model is that it is consistent with
basic economic theory; the Tale of the Long Tail’s
model is not. Revenues are not determined by
an opening week penetration rate: they are
determined by the number of theaters (or
screens) a movie is in.25 Nor are revenues from
blockbusters lower than the revenues from small
or mid-sized films.
Why Not Theaters?
Why didn’t the authors of Tale of the Long Tail
just use the number of theaters for each
weekend instead of the size variable? It is
obvious that weekend revenues are determined
mostly (about 87%) by the number of the
theaters in which the movie plays. Economic
theory certainly points to the use of theaters or
screens.26
Theft is not normally viewed as
beneficial to the victim. Tale of the
Long Tail’s take on piracy, however,
suggests otherwise, and this result
should be a “red flag” to perform
careful diagnostics on the model
before touting its findings. Having
done so, it seems readily apparent
that the counter-intuitive result
found in Tale of the Long Tail is not
“fact” but “artifact.”
The argument provided in Tale of the Long Tail is
that the “absolute number of screens per
country per week [is] potentially endogenous to
the shutdown because theater owners can
quickly adjust the number of screens as a
response to changes in demand.”27
The
argument is unexplained and, in my view,
makes no sense. Indeed, the fact that theater
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P E R S P E C T I V E S
owners adjust the number of theaters to changes
in demand is the reason why revenues are so
successfully modeled as a function of the
number of theaters. Such responses are the data
generating process because they reflect the
profit-maximizing behavior of exhibitors.
If it is true that the number of theaters is
“endogenous to the shutdown,” then why
doesn’t the study model that process, including
the multiple equations implied by the argument,
or at least provide a rigorous demonstration as
to why the revenue equation can be estimated
alone? If the variable is in fact endogenous and
relevant, then the proper method is to include it
and apply proper statistical methods to deal
with endogeneity. Moreover, replacing the
number of theaters with opening week theaters
is not a solution at all. The movie industry
selects the number of theaters in which to play a
movie based on expectations, so the opening
number of screens is just as endogenous as the
actual number of screens per weekend.
Furthermore, the endogeneity argument would
be equally valid for the number of weeks a
movie is screened as it would for the number of
theaters in which the movie appears, yet the
authors include that variable in the analysis.28
Conclusion
Theft is not normally viewed as beneficial to the
victim. Tale of the Long Tail’s take on piracy,
however, suggests otherwise, and this result
should be a “red flag” to perform careful
diagnostics on the model before touting its
findings. Having done so, it seems readily
apparent that the counter-intuitive result found
in Tale of the Long Tail is not “fact” but “artifact.”
In this PERSPECTIVE, I have pointed out one
major defect in the study, but there are many
more problems. Indeed, the improbable result is
the consequence of the compounding of poor
modeling choices, and a neglect of the basic
economics of the movie industry. Given the
unreasonable implications of the model, Tale of
the Long Tail adds nothing constructive to the
debate—save a little excitement.
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NOTES:

Dr. George S. Ford is the Chief Economist of the Phoenix Center for Advanced Legal and Economic Public Policy
Studies. The views expressed in this PERSPECTIVE do not represent the views of the Phoenix Center or its staff.
C. Peukert, J. Claussen, and T. Kretschmer, Piracy and Movie Revenues: Evidence from Megaupload: A Tale of the Long Tail?,
Unpublished Working Paper (August 20, 2013) (hereinafter “Tale of the Long Tail”) (available at:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2176246).
1
B. Sisario, 7 Charged as FBI Closes a Top File-Sharing Site, NEW YORK TIMES (January 19, 2012) (available at:
http://www.nytimes.com/2012/01/20/technology/indictment-charges-megaupload-site-with-piracy.html).
2
In order to estimate the fixed-effects model of the study (that is, to identify the shutdown variable), some movies must
be in theaters both before and after the shutdown date (and this crossover could occur across countries).
3
B. Danaher and M D. Smith, Gone in 60 Seconds: The Impact of the Megaupload Shutdown on Movie Sales, Working Paper
(March 6, 2013)(available at: http://ssrn.com/abstract=2229349).
4
See, e.g., C. Dewey, Study: Piracy Actually Helps Small Films Make Money, WASHINGTON POST (August 26, 2013) (available
at:
http://www.washingtonpost.com/blogs/the-switch/wp/2013/08/26/study-piracy-actually-helps-small-films-makemoney); D. Cohen, Closing Piracy Powerhouse Actually Hurt Movie Revenues, VARIETY (August 27, 2013) (available at:
http://variety.com/2013/digital/news/megaupload-closing-piracy-hurt-film-revenues-1200590076); L. Bahr, Study Suggest
Piracy Might Be Good For Indies, Bad For Blockbusters, ENTERTAINMENT WEEKLY (August 27, 2013) (available at:
http://insidemovies.ew.com/2013/08/27/piracy-study).
5
6
See, e.g., G. Tullock, The Welfare Costs of Tariffs, Monopolies, and Theft, 5 WESTERN ECONOMIC JOURNAL 224-232 (1967).
7
Computed based on estimates from the “Pre” period at S = 1 and S = 0.57.
These problems are both statistical and practical. Some issues include the fact that the variable measuring
Megaupload’s popularity across countries is based on data from only after the shutdown, not before when the popularity of
the site matters most to piracy. Also, it appears that many of the movies in the sample were not available on pirating sites
during their box office run.
8
9
Since a movie can show on multiple screens (e.g., standard and 3D versions), screens is probably the preferred measure.
10
The sample is from boxofficemojo.com.
11
I suspect the explanatory power of the model may be even higher with data on screens.
12
Tale of the Long Tail, supra n. 1 at p. 12 (“A value of 1 indicates that a movie has the largest all-time first-week audience in
a given country.”). There are potentially serious problems with this approach, including serving as the source for the odd
result discussed here, but a detailed analysis of that issue is not possible without all the data and it’s not the main issue of
discussion now.
13
Id. at pp. 8, 12.
14
Id. at p. 12 (“We find the expected non-linear relationship with a maximum of 0.57.”)
This interpretation of the result is consistent with the description provided in the study. Tale of the Long Tail, id. at p. 145, discussing Figure 5. Another interpretation of Figure 2 is that is represents the relationship between revenues and the
penetration rate of opening theaters (S) for a representative movie, not for different movies. In this view, the relationship
suggests a movie will earn more money if its opens in fewer rather than more theaters; an unreasonable and counter-factual
finding. Thus, there is no solace in this alternative interpretation. Notably, it appears that the relationship between
revenues and S arises solely from the cross-country variation in S, which could be the source of the peculiar relationship
between revenues and size. With movie fixed effects, the S variable can’t be estimated for an individual country, since the
movie fixed effect and S are collinear.
15
16
The value of the “Pre” curve is 1.07 (ignoring the constants) for S values of 1 and 0.144.
17
For example, the 2009 film Avatar could have increased its revenues by nearly 30% by opening in 25% fewer theaters.
PHOENIX CENTER PERSPECTIVES 13-05
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NOTES CONTINUED:
18
The bands are 600-800 theaters, 2400-2600 theaters, and greater than 4,250 theaters.
19
The U.S. data suggests the presence of multiple countries in the sample is a potential cause of the problem.
20
The shape of the Post curve is determined by: 0.22 + (8.56-2.61)S + (-7.49+3.07)S2.
21
Tale of the Long Tail, supra n. 1 at p. 15. Statistically, the only relationship shown to be non-zero is the effect on middlesized S values. While both small-and-large S films have positive values, the authors are unable to conclude that the effect is
not zero due to the wide confidence bands, which are not shown in the figure. Confidence intervals are tighter closer to the
mean of the data, so the wider intervals at the extremes of S are expected.
22
This scenario is easily demonstrated using a Monte Carlo study.
23
For consistency with Tale of the Long Tail, I include calendar week and year fixed effects.
Goodness of fit is not the only determinant of a well-specified model. The revenue-to-theater model is consistent with
theory and fits the data; the Tale of the Long Tail’s specification does not.
24
The model also includes a measure of weeks the movie has played, which is correlated with theater count (one is falling
over time, the other rising). Still, this decay rate is not uniform across films, and the opening week is not always consistent
with the true “size” of a film.
25
Forcing common slope coefficients across all countries is suspect. Even so, the model could have estimated separate
coefficients for countries with theater data and for countries with screen data, creating only two sets of coefficients.
26
27
Tale of the Long Tail, supra n. 1 at p. 15.
28
To see this, consider a slight modification of the authors’ claim about theaters: “the absolute number of [weeks] [is]
potentially endogenous to the shutdown because theater owners can quickly adjust the [number of week] as a response to
changes in demand.” Id.
PHOENIX CENTER PERSPECTIVES 13-05
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